Scale Vertices - to a common center
A person who designs type calls the width of the individual bits of a character design a "stroke". I know of two ways to deal with the problem you are trying to solve, that is changing the width of the stroke. The first is to use a different font. If you are wanting the general shape of the characters of the font with a different width stroke, you can sometimes find a different font designed like that from the outset. There are different words used as modifiers to font names to indicate variations from standard font design. The words "light" and "medium" are two of the terms used in a font name to indicate the font has the same sized characters with a thinner stroke, and these terms are sometimes modified further by "ultra" or "extra". On the opposite end of the spectrum, the words "heavy" and "bold" are used to denote fonts where the characters are the same size, but have thicker strokes. While it is not germane to the question originally posed, for sake of completeness of the answer, "light", "medium", "heavy" and "bold" refer to the width of the stroke, and the width of the overall character itself is generally relatively constant. There are fonts where the stroke size is relatively unchanged, but the overall width of the character is changed. When the width is smaller, the word "condensed" is used, and when the width is larger, the word "extended" is used, and "ultra" or "extra" may be applied to these as well. So "Helvetica light" is a font with narrower stroke sizes in the character; "Helvetica extra bold extended" is a font with wider characters, and a wider stroke. It should be noted that in use of type, the overall height, as measured from the bottom of a descender (like lower case p, j, q, or y) to the top of an ascender (like lower case l, b, and d") is more or less constant across all fonts, although certain dimensions within the font, such as "x height" may a vary from one font to the next.

So, if you want a font with a narrower stroke, the best bet is to determine this in advance, and obtain a light version of the font you wish to use, if it is available. That would be my default choice.

But, if for some reason I wanted to change the stroke width of a character, the way I would proceed is to do each character by subsections. In the case of the "e", what I would do first is to select all of the vertices forming the inside of the curve of the character, and with setting the pivot point at "median", scale these vertices outward by the desired amount. Next, I would select the vertices forming the top of the bar of the e, and instead of scaling the bar, I would move the upper part of the cross bar so that the bar is proportional to the relationship between the bar and the circular part of the letter before you started changing it. Assuming that you are using the Text facility in Blender, if the changes you want to make will result in a different overall height of the font, I would achieve this by changing the font size using the "size" entry bar in the Font panel of the Font object data editor of the Properties editor.

Note that in nearly all fonts, the horizontal bits of the font, like the crossbar of the e, the cross of the t, &amp;c. are uniform, but vertical and diagonal strokes making up characters are not uniform; The upper case "M" "W" and "X" almost always have two different widths of strokes. This difference in stroke widths forms an essential part of the identity of the font, so the "X" may need to be done in two steps.